Dimension and extensions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam
North Holland
1993
|
| Schriftenreihe: | North-Holland mathematical library
v. 48 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned. With the classical dimension theory as a model, the inductive, covering and basic aspects of the dimension functions are investigated in this volume, resulting in extensions of the sum, subspace and decomposition theorems and theorems about mappings into spheres. Presented are examples, counterexamples, open problems and solutions of the original and modified compactification problems Includes bibliographical references (p. 315-326) and index |
| Beschreibung: | 1 Online-Ressource (xii, 331 p.) |
| ISBN: | 9780444897404 0444897402 9780080887616 0080887619 1281778966 9781281778963 |
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| 490 | 0 | |a North-Holland mathematical library |v v. 48 | |
| 500 | |a Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned. With the classical dimension theory as a model, the inductive, covering and basic aspects of the dimension functions are investigated in this volume, resulting in extensions of the sum, subspace and decomposition theorems and theorems about mappings into spheres. Presented are examples, counterexamples, open problems and solutions of the original and modified compactification problems | ||
| 500 | |a Includes bibliographical references (p. 315-326) and index | ||
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| 650 | 4 | |a Dimension theory (Topology) | |
| 650 | 4 | |a Mappings (Mathematics) | |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Aarts, J. M. 1938-2018 |
| author_GND | (DE-588)1077023162 |
| author_facet | Aarts, J. M. 1938-2018 |
| author_role | aut |
| author_sort | Aarts, J. M. 1938-2018 |
| author_variant | j m a jm jma |
| building | Verbundindex |
| bvnumber | BV042317580 |
| collection | ZDB-33-ESD ZDB-33-EBS |
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| dewey-full | 514/.32 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.32 |
| dewey-search | 514/.32 |
| dewey-sort | 3514 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:18:17Z |
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| isbn | 9780444897404 0444897402 9780080887616 0080887619 1281778966 9781281778963 |
| language | English |
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| spelling | Aarts, J. M. 1938-2018 Verfasser (DE-588)1077023162 aut Dimension and extensions J.M. Aarts, T. Nishiura Amsterdam North Holland 1993 1 Online-Ressource (xii, 331 p.) txt rdacontent c rdamedia cr rdacarrier North-Holland mathematical library v. 48 Two types of seemingly unrelated extension problems are discussed in this book. Their common focus is a long-standing problem of Johannes de Groot, the main conjecture of which was recently resolved. As is true of many important conjectures, a wide range of mathematical investigations had developed, which have been grouped into the two extension problems. The first concerns the extending of spaces, the second concerns extending the theory of dimension by replacing the empty space with other spaces. The problem of de Groot concerned compactifications of spaces by means of an adjunction of a set of minimal dimension. This minimal dimension was called the compactness deficiency of a space. Early success in 1942 lead de Groot to invent a generalization of the dimension function, called the compactness degree of a space, with the hope that this function would internally characterize the compactness deficiency which is a topological invariant of a space that is externally defined by means of compact extensions of a space. From this, the two extension problems were spawned. With the classical dimension theory as a model, the inductive, covering and basic aspects of the dimension functions are investigated in this volume, resulting in extensions of the sum, subspace and decomposition theorems and theorems about mappings into spheres. Presented are examples, counterexamples, open problems and solutions of the original and modified compactification problems Includes bibliographical references (p. 315-326) and index Topological spaces Topologia larpcal Compactifications fast Dimension theory (Topology) fast Mappings (Mathematics) fast MATHEMATICS / Topology bisacsh Dimension theory (Topology) Mappings (Mathematics) Compactifications Dimensionstheorie (DE-588)4149935-9 gnd rswk-swf Kompaktifizierung (DE-588)4164859-6 gnd rswk-swf Kompaktifizierung (DE-588)4164859-6 s 1\p DE-604 Dimensionstheorie (DE-588)4149935-9 s 2\p DE-604 Nishiura, Togo Sonstige oth http://www.sciencedirect.com/science/book/9780444897404 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Aarts, J. M. 1938-2018 Dimension and extensions Topological spaces Topologia larpcal Compactifications fast Dimension theory (Topology) fast Mappings (Mathematics) fast MATHEMATICS / Topology bisacsh Dimension theory (Topology) Mappings (Mathematics) Compactifications Dimensionstheorie (DE-588)4149935-9 gnd Kompaktifizierung (DE-588)4164859-6 gnd |
| subject_GND | (DE-588)4149935-9 (DE-588)4164859-6 |
| title | Dimension and extensions |
| title_auth | Dimension and extensions |
| title_exact_search | Dimension and extensions |
| title_full | Dimension and extensions J.M. Aarts, T. Nishiura |
| title_fullStr | Dimension and extensions J.M. Aarts, T. Nishiura |
| title_full_unstemmed | Dimension and extensions J.M. Aarts, T. Nishiura |
| title_short | Dimension and extensions |
| title_sort | dimension and extensions |
| topic | Topological spaces Topologia larpcal Compactifications fast Dimension theory (Topology) fast Mappings (Mathematics) fast MATHEMATICS / Topology bisacsh Dimension theory (Topology) Mappings (Mathematics) Compactifications Dimensionstheorie (DE-588)4149935-9 gnd Kompaktifizierung (DE-588)4164859-6 gnd |
| topic_facet | Topological spaces Topologia Compactifications Dimension theory (Topology) Mappings (Mathematics) MATHEMATICS / Topology Dimensionstheorie Kompaktifizierung |
| url | http://www.sciencedirect.com/science/book/9780444897404 |
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